SSC CGL 2025 Tier-II · Paper-I, 19 January 2026 · Mathematical Abilities · Question 27 of 150

We transcribed this text from the pictures of a candidate's response sheet for this paper; the answer is the key SSC marked with a green tick on that sheet. Solution last reviewed 11 September 2026.

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SSC does not publish CGL question papers or a public answer key. This paper reaches us as a candidate's response sheet saved as pictures, so we transcribed the text from those pictures, and a second reader checked every question against them; where the layout carries meaning, we show the picture too. Each answer is the key SSC marked with a green tick on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. UnlockIAS wrote the solutions.

If the mode of the data set {a, a + 2, a + 4, a + 6, a + 6, a + 6, a + 8} is 26, find a.

(a)40
(b)20
(c)30
(d)10

Answer

Why

Correct — B. The mode is the value that repeats most often.

Count repeats: a + 6 appears three times, every other term once
So the mode = a + 6

Set it equal to the given mode: a + 6 = 26
Subtract 6 from both sides: a = 20

Check: the set is 20, 22, 24, 26, 26, 26, 28, and 26 repeats most → option (b)

Why the others are wrong

(a)
40 — a = 40 makes the set 40, 42, 44, 46, 46, 46, 48. Its mode is 46, not 26.
(c)
30 — a = 30 makes a + 6 = 36 the repeated value, so the mode would be 36, ten more than the given 26.
(d)
10 — a = 10 gives a mode of 10 + 6 = 16, ten short of the given 26.

Concept

The mode is the observation with the highest frequency. When the data are written in terms of a variable, the mode is whichever expression repeats most, here a + 6.

Equate that expression to the given value and solve for the variable.

In this set the median is also a + 6, the 4th of seven ordered terms, so mixing up mode and median would still give 20 here. The mean is a + 32⁄7, and setting that to 26 gives a ≈ 21.4, which is not offered.

Key facts

Mode = the most frequent value in a data set.
For an odd number n of ordered values, the median is the ((n + 1)⁄2)th value.
Adding the same constant to every value shifts the mean, median and mode by that constant.

Study next

Mean and median of data written in terms of a variableData sets with two modes (bimodal data)The empirical relation Mode ≈ 3 Median − 2 Mean for moderately skewed data

Common traps

Adding 6 instead of subtracting it: 26 + 6 = 32.
Setting the mean to 26 instead of the mode.

The mode also appears at 19 Jan 2026, 11:00 AM, Maths Q.23, from a plain list of nine marks, and at 13 Sep 2024, 12:30, Quant Q.1, from a bar graph of children's ages.

Related PYQs

No directly related past PYQ was found.

Topic: Statistics and probability — all 6 SSC CGL questions on it, every solved shift.